Question

Consider the hypotheses below. Upper H 0​: mu equals 50 Upper H 1​: mu not equals 50 Given that x overbar equals 60​, s equals 12​, nequals30​, and alphaequals0.10​, answer the questions below. a. What conclusion should be​ drawn? b. Use technology to determine the​ p-value for this test. a. Determine the critical​ value(s). The critical​ value(s) is(are) 1.311. ​(Round to three decimal places as needed. Use a comma to separate answers as​ needed.)

Answer 1

Answer:

We conclude that  $\mu\neq$ 50.

Step-by-step explanation:

We are given that x bar = 60​, s = 12​, n = 30​, and alpha = 0.10

Also, Null Hypothesis, $H_0$ : $\mu$ = 50

Alternate Hypothesis, $H_1$ : $\mu$ $\neq$ 50

The test statistics we will use here is;

                    T.S. = $\frac{Xbar-\mu}{\frac{s}{\sqrt{n} } }$ ~  $t_n_-_1$

where, X bar = sample mean = 60

              s = sample standard deviation = 12

              n = sample size = 30

So, Test statistics = $\frac{60-50}{\frac{12}{\sqrt{30} } }$ ~ $t_2_9$

                             = 4.564

At 10% significance level, t table gives critical value of 1.311 at 29 degree of freedom. Since our test statistics is more than the critical value as 4.564 > 1.311 so we have sufficient evidence to reject null hypothesis as our test statistics will fall in the rejection region.

P-value is given by, P($t_2_9$ > 4.564) = less than 0.05% {using t table}

Here also, P-value is less than the significance level as 0.05% < 10% , so we will reject null hypothesis.

Therefore, we conclude that $\mu\neq$ 50.